Minimizing CM degree and slope stability of projective varieties

Abstract

We discuss a minimization problem of the degree of the CM line bundle among all possible fillings of a polarized family with fixed general fibers. We show that such minimization implies the slope semistability of the fiber if the central fiber is smooth.

14 pages

References in corpus (6)

• A generalization of Ross-Thomas' slope theory
• Stability of Valuations and Kollár Components
• On the moduli of Kahler-Einstein Fano manifolds
• A note on the definition of K-stability
• Nonexistence of asymptotic GIT compactification
• Uniqueness of K-polystable degenerations of Fano varieties

Cited by in corpus (1)

• PL density invariant for type II degenerating K3 surfaces, Moduli compactification and hyperKahler metrics